Comparison of two replacement policies

1986 ◽  
Vol 23 (3) ◽  
pp. 759-769 ◽  
Author(s):  
Antonín Lešanovský
Keyword(s):  
Finite Number ◽  
Discrete Time ◽  
Optimal Replacement

Two models of a system with a single activated unit which can be in a finite number of states are considered. The unit is subject to Markovian deterioration, and it is possible to replace it before its failure. Inspections of the system are carried out at discrete time instants. The only difference between the two models is when the replacements take effect — immediately at the instant when the corresponding decision is made, or with the next inspection. The paper shows that this difference is much more essential than one might expect, and proves a relation between the optimal replacement strategies in the models concerned.

Comparison of two replacement policies

1986 ◽  
Vol 23 (03) ◽  
pp. 759-769 ◽  
Author(s):  
Antonín Lešanovský
Keyword(s):  
Finite Number ◽  
Discrete Time ◽  
Optimal Replacement

Two models of a system with a single activated unit which can be in a finite number of states are considered. The unit is subject to Markovian deterioration, and it is possible to replace it before its failure. Inspections of the system are carried out at discrete time instants. The only difference between the two models is when the replacements take effect — immediately at the instant when the corresponding decision is made, or with the next inspection. The paper shows that this difference is much more essential than one might expect, and proves a relation between the optimal replacement strategies in the models concerned.

Estimation of Steady-State Optimal Filter Gain From Nonoptimal Kalman Filter Residuals

1994 ◽  
Vol 116 (3) ◽  
pp. 550-553 ◽  
Author(s):  
Chung-Wen Chen ◽  
Jen-Kuang Huang
Keyword(s):  
Kalman Filter ◽  
Steady State ◽  
Finite Number ◽  
Discrete Time ◽  
Stochastic System ◽  
Moving Average ◽  
Ar Model ◽  
Numerical Example ◽  
Measurement Noises ◽  
Time Invariant

This paper proposes a new algorithm to estimate the optimal steady-state Kalman filter gain of a linear, discrete-time, time-invariant stochastic system from nonoptimal Kalman filter residuals. The system matrices are known, but the covariances of the white process and measurement noises are unknown. The algorithm first derives a moving average (MA) model which relates the optimal and nonoptimal residuals. The MA model is then approximated by inverting a long autoregressive (AR) model. From the MA parameters the Kalman filter gain is calculated. The estimated gain in general is suboptimal due to the approximations involved in the method and a finite number of data. However, the numerical example shows that the estimated gain could be near optimal.

Equivalence of two absorption problems with Markovian transitions and continuous or discrete time parameters

1959 ◽  
Vol 55 (2) ◽  
pp. 177-180 ◽  
Author(s):  
R. A. Sack
Keyword(s):  
Finite Number ◽  
Markov Processes ◽  
Discrete Time ◽  
Continuous Time ◽  
Time Parameter ◽  
Rate Of Change ◽  
Matrix Form ◽  
Constant Matrix ◽  
Time Parameters ◽  
Image Position

1. Introduction. Ledermann(1) has treated the problem of calculating the asymptotic probabilities that a system will be found in any one of a finite number N of possible states if transitions between these states occur as Markov processes with a continuous time parameter t. If we denote by pi(t) the probability that at time t the system is in the ith state and by aij ( ≥ 0) the constant probability per unit time for transitions from the jth to the ith state, the rate of change of pi is given bywhere the sum is to be taken over all j ≠ i. This set of equations can be written in matrix form aswhere P(t) is the vector with components pi(t) and the constant matrix A has elements

scholarly journals Recursive estimation of inventory quality classes using sampling

2003 ◽  
Vol 7 (4) ◽  
pp. 249-263 ◽  
Author(s):  
L. Aggoun ◽  
L. Benkherouf ◽  
A. Benmerzouga
Keyword(s):  
Finite Number ◽  
Discrete Time ◽  
Lower Class ◽  
Inventory Model ◽  
Recursive Estimation ◽  
Single Product ◽  
Discrete State ◽  
Perishable Items ◽  
Optimal Estimates ◽  
Class 1

In this paper we propose a new discrete time discrete state inventory model for perishable items of a single product. Items in stock are assumed to belong to one of a finite number of quality classes that are ordered in such a way that Class 1 contains the best quality and the last class contains the pre-perishable quality. By the end of each epoch, items in each inventory class either stay in the same class or lose quality and move to a lower class. The movement between classes is not observed. Samples are drawn from the inventory and based on the observations of these samples, optimal estimates for the number of items in each quality classes are derived.

scholarly journals Extending the CGLS method for finding the least squares solutions of general discrete-time periodic matrix equations

Filomat ◽  
2016 ◽  
Vol 30 (9) ◽  
pp. 2503-2520 ◽  
Author(s):  
Masoud Hajarian
Keyword(s):  
Finite Number ◽  
Least Squares ◽  
Control Systems ◽  
Discrete Time ◽  
Conjugate Gradient ◽  
Matrix Form ◽  
Matrix Equations ◽  
Numerical Examples ◽  
Periodic Matrix ◽  
Time Periodic

The periodic matrix equations are strongly related to analysis of periodic control systems for various engineering and mechanical problems. In this work, a matrix form of the conjugate gradient for least squares (MCGLS) method is constructed for obtaining the least squares solutions of the general discrete-time periodic matrix equations ?t,j=1 (Ai,jXi,jBi,j + Ci,jXi+1,jDi,j)=Mi, i=1,2,.... It is shown that the MCGLS method converges smoothly in a finite number of steps in the absence of round-off errors. Finally two numerical examples show that the MCGLS method is efficient.

General transition probabilities for finite Markov chains

1964 ◽  
Vol 60 (1) ◽  
pp. 83-91 ◽  
Author(s):  
Marcel F. Neuts
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Finite Number ◽  
Discrete Time ◽  
Transition Probabilities ◽  
Initial State ◽  
Discrete Time Markov Chain ◽  
Finite Markov Chains

We consider a stationary discrete-time Markov chain with a finite number m of possible states which we designate by 1,…,m. We assume that at time t = 0 the process is in an initial state i with probability (i = 1,…, m) and such that and .

Optimal Replacement in a Discrete time Shock Model

OPSEARCH ◽  
1998 ◽  
Vol 35 (4) ◽  
pp. 338-345 ◽  
Author(s):  
Asok K. Nanda
Keyword(s):  
Discrete Time ◽  
Shock Model ◽  
Optimal Replacement

scholarly journals A Quantum Time Coordinate

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 306
Author(s):  
Armando Martínez-Pérez ◽  
Gabino Torres-Vega
Keyword(s):  
Finite Number ◽  
Coordinate System ◽  
Discrete Time ◽  
Box Model ◽  
Time Coordinate ◽  
Energy Eigenstates ◽  
High Energies ◽  
Quantum Time ◽  
Classical Transition ◽  
The Many

We discuss quantum time states formed with a finite number of energy eigenstates with the purpose of obtaining a time coordinate. These time states are eigenstates of the recently introduced discrete time operator. The coordinate and momentum representations of these time eigenstates resemble classical time curves and become classical at high energies. To illustrate this behavior, we consider the simple example of the particle-in-a-box model. We can follow the quantum-classical transition of the system. Among the many existing solutions for the particle in a box, we use a set which leads to time eigenstates for use as a coordinate system.

EXACT STATE RECONSTRUCTORS IN THE RECOVERY OF MESSAGES ENCRYPTED BY THE STATES OF NONLINEAR DISCRETE-TIME CHAOTIC SYSTEMS

2002 ◽  
Vol 12 (01) ◽  
pp. 169-177 ◽  
Author(s):  
HEBERTT SIRA-RAMÍREZ ◽  
CARLOS AGUILAR IBÁÑEZ ◽  
MIGUEL SUÁREZ-CASTAÑÓN
Keyword(s):  
Finite Number ◽  
State Estimation ◽  
Discrete Time ◽  
Chaotic Systems ◽  
Estimation Error ◽  
Color Images ◽  
The Internet ◽  
System State ◽  
State Reconstruction ◽  
Efficient Decoding

In this article we propose the use of nonlinear exact chaotic system state reconstructors for the fast and efficient decoding of multiple discrete-time chaotic encrypted digital messages. Exact state reconstruction features a state estimation error which settles to zero in a finite number of steps. This makes the method specially suitable for chaotic encrypted transmission of digitized files over "noise-free" environments such as the Internet. The method was tested in an actual transmission involving the simultaneous decoding of digitized color images and text files.

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